“direction ratios”的概念、定义、翻译、参考文献-科学参考

direction ratios

Mathematics

Suppose that a direction has direction cosines cosα‎, cosβ‎, cosγ‎. Any triple of numbers l, m, n, not all zero, such that l = k cosα‎, m = k cosβ‎, n = k cosγ‎, are called direction ratios of the given direction. Since cos²α‎ + cos²β‎ + cos²γ‎ = 1, it follows that

$\begin{array}{l} cos α = \frac{\pm l}{\sqrt{l^{2} + m^{2} + n^{2}}}, cos β = \frac{\pm m}{\sqrt{l^{2} + m^{2} + n^{2}}}, \\ cos γ = \frac{\pm n}{\sqrt{l^{2} + m^{2} + n^{2}}}, \end{array}$

where either the + sign or the − sign is taken throughout. So any triple of numbers, not all zero, determine two possible sets of direction cosines, corresponding to opposite directions. The triple l, m, n are said to be direction ratios of a straight line when they are direction ratios of either direction of the line.

单词	direction ratios
释义	direction ratios Mathematics Suppose that a direction has direction cosines cosα‎, cosβ‎, cosγ‎. Any triple of numbers l, m, n, not all zero, such that l = k cosα‎, m = k cosβ‎, n = k cosγ‎, are called direction ratios of the given direction. Since cos²α‎ + cos²β‎ + cos²γ‎ = 1, it follows that $\begin{array}{l} cos α = \frac{\pm l}{\sqrt{l^{2} + m^{2} + n^{2}}}, cos β = \frac{\pm m}{\sqrt{l^{2} + m^{2} + n^{2}}}, \\ cos γ = \frac{\pm n}{\sqrt{l^{2} + m^{2} + n^{2}}}, \end{array}$ where either the + sign or the − sign is taken throughout. So any triple of numbers, not all zero, determine two possible sets of direction cosines, corresponding to opposite directions. The triple l, m, n are said to be direction ratios of a straight line when they are direction ratios of either direction of the line.
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